Preheat your oven to 375 degrees F and line a baking sheet with parchment paper. Set aside.
In a small saucepan, melt the butter and shortening over low heat. Remove from heat and set aside to cool slightly.
In a large bowl, whisk together the flour, baking powder and salt. Set aside.
Add the melted butter and shortening to the bowl of your stand mixer and add the sugar. Mix until combined, about 30 seconds. Add each egg, one at a time, until they are incorporated. Add the anise extract (or vanilla; or lemon) and mix again until combined.
In half cup increments, add the dry ingredients into the wet. Mix to combine until a soft dough forms. The dough will be soft, but still manageable. If it isn''t manageable (where you can work it into a teaspoon-sized ball without making a mess), add tablespoons (one at a time) of flour until you reach this consistency.
Once your dough is ready, pinch of pieces of dough and roll into 3/4 - 1 inch balls. Place the balls on your baking sheet, spacing them at least 1 inch apart. Bake at 375 degrees F for 7-8 minutes until they just begin to brown on the bottoms and just begin to crack slightly on top. Remove from oven and transfer to a wire rack to cool completely. Repeat this step for the rest of your dough.
While your cookies are cooling, prepare the glaze. In a bowl, whisk together the confectioner''s sugar, anise extract (or vanilla; or lemon) and half and half. You want the glaze to be on the heavier side.
When your cookies have cooled completely, dip the top of each cookie in the glaze and place back on the wire rack to set. Decorate with sprinkles or sugar immediately before the glaze hardens.
Store in an airtight container for a week or two. Enjoy!